Problem: Express your answer as a mixed number simplified to lowest terms. $10\dfrac{2}{7}-3\dfrac{1}{3} = {?}$
Solution: Find a common denominator for the fractions: $= {10\dfrac{6}{21}}-{3\dfrac{7}{21}}$ Convert ${10\dfrac{6}{21}}$ to ${9 + \dfrac{21}{21} + \dfrac{6}{21}}$ So the problem becomes: ${9\dfrac{27}{21}}-{3\dfrac{7}{21}}$ Separate the whole numbers from the fractional parts: $= {9} + {\dfrac{27}{21}} - {3} - {\dfrac{7}{21}}$ Bring the whole numbers together and the fractions together: $= {9} - {3} + {\dfrac{27}{21}} - {\dfrac{7}{21}}$ Subtract the whole numbers: $=6 + {\dfrac{27}{21}} - {\dfrac{7}{21}}$ Subtract the fractions: $= 6+\dfrac{20}{21}$ Combine the whole and fractional parts into a mixed number: $= 6\dfrac{20}{21}$